Method of feedback control of ESC voltage using wafer voltage measurement at the bias supply output

ABSTRACT

In a plasma reactor having an electrostatic chuck, wafer voltage is determined from RF measurements at the bias input using previously determined constants based upon transmission line properties of the bias input, and this wafer voltage is used to accurately control the DC wafer clamping voltage.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.11/127,036, filed May 10, 2005 entitled DUAL BIAS FREQUENCY WITHFEEDBACK CONTROL OF E.S.C. VOLTAGE USING WAFER VOLTAGE MEASUREMENT ATTHE BIAS SUPPLY OUTPUT by Jang Gyoo Yang, et al. and assigned to thepresent assignee.

BACKGROUND OF THE INVENTION

A plasma reactor for processing a semiconductor wafer typically holdsthe wafer inside the reactor chamber using an electrostatic chuck (ESC).Plasma ion energy at the wafer surface is controlled by applying a biasvoltage to the wafer through the ESC. The ESC essentially consists of aninsulator layer having a top surface for supporting the wafer. Anelectrode or conductive mesh inside the insulator layer beneath thewafer receives a D.C. voltage, creating a voltage drop across theinsulator layer between the electrode and the wafer, which produces anelectrostatic force clamping the wafer to the ESC. The clamping force isdetermined by the difference between the time-average of the wafervoltage and the D.C. voltage applied to the ESC electrode. The clampingvoltage must be accurately controlled (by accurately controlling theD.C. supply voltage) in order to avoid an insufficient clamping voltageor an excessive clamping voltage. An insufficient clamping voltage wouldallow the wafer to pop off of the ESC. An excessive clamping voltagewould increase the current through the wafer to a level that risksdamaging the circuit features formed on the wafer surface. (Currentflows from the ESC electrode through the dielectric layer to the waferand returns through the plasma in the chamber. The stronger the clampingforce, the greater the conductivity between the wafer and the ESC, andtherefore the greater the current through the wafer.) In order toaccurately control the clamping voltage, the wafer D.C. voltage must bemeasured accurately. An error in wafer voltage measurement may lead towafer pop off or to excessive ESC-wafer current.

Use of ESC-wafer contact to control the wafer temperature imposes evenmore stringent requirements for accurate control of clamping voltage. Asdisclosed in co-pending U.S. patent application Ser. No. 10/929,104,filed Aug. 26, 2004 entitled, “Gasless High Voltage High Contact ForceWafer Contact-Cooling Electrostatic Chuck,” by Douglas Buchberger, Jr.et al., and assigned to the present assignee, the ESC may be heated orcooled so that the wafer is either heated or cooled at a rate determinedby the ESC clamping force. The wafer temperature may therefore beaccurately set and controlled as desired. In fact, the heat transferrate is so great as the clamping voltage is increased, that the wafertemperature may be maintained under much higher heat load than wasformerly possible. Thus, for example, the wafer bias power may beincreased beyond previously permitted levels. However, the wafertemperature range is limited because the clamping voltage cannot closelyapproach the upper limit (above which the wafer current is excessive) orthe lower limit (below which the wafer may pop off the ESC), withoutmore accurate determination of wafer voltage. (The clamping voltage isdetermined from the difference between the time average of the wafervoltage and the D.C. supply voltage.) Current methods for estimatingwafer voltage tend to be inaccurate, so that the clamping voltage rangemust be limited to ensure that wafer voltage measurement errors do notcause the clamping voltage to violate the upper and lower limits.

An accurate method for determining wafer voltage is disclosed inco-pending U.S. patent application Ser. No. 10/440,364, filed May 16,2003 by Daniel Hoffman and assigned to the present assignee. This methodis applicable to a plasma reactor in which bias power of a single biasfrequency only is coupled to the wafer from the ESC. This method isinaccurate when more than one bias frequency is present. For example,the reactor may apply bias power having a low frequency (LF) componentand a high frequency (HF) component in order to obtain a favorable ionenergy distribution for a plasma process such as plasma enhance reactiveion etching. A large error in wafer voltage measurement occurs when sucha dual frequency bias is employed. We have found that the error in thewafer voltage measurement in such a case can create a clamping voltageerror exceeding the capacity of the ESC's D.C. voltage supply.

What is needed is an accurate way of measuring wafer voltage with a dualfrequency bias. This would permit the clamping voltage to be set tovalues closer either the maximum or minimum allowed clamping voltagewithout fear of violating these limits due to wafer voltage measurementerrors. This in turn permits the wafer temperature range to be expandedaccordingly, a significant advantage.

SUMMARY OF THE INVENTION

In a plasma reactor having an electrostatic chuck (ESC) supporting awafer to be processed, a method of processing the wafer whilecontrolling an ESC clamping voltage includes applying RF bias power tothe ESC from a bias power source at an input to the ESC and applying aD.C. voltage at the input to the ESC from a D.C. voltage source. Thevoltage and current is measured near the input to produce a measuredvoltage and a measured current. A wafer voltage signal is provided as asum of the measured voltage and the measured current multiplied by firstand second coefficients respectively, the wafer voltage signalrepresenting the voltage on a wafer supported on the ESC. The methodfurther includes computing a wafer clamping voltage as a differencebetween a D.C. component of the wafer voltage signal and the D.C.voltage from the D.C. voltage source, and controlling the D.C. voltageto regulate the wafer clamping voltage. In one embodiment, controllingthe D.C. voltage is performed so as to minimize a difference between thewafer clamping voltage and a target clamping voltage.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates a plasma reactor with a measurement instrument in anelectrostatic chuck feedback control loop, the reactor having a biasvoltage source with a low frequency (LF) component and a high frequency(HF) component.

FIG. 1B is a block diagram of apparatus within the measurementinstrument for determining wafer voltage based upon the HF and LFcomponents of the bias supply voltage and current for the feedbackcontrol loop.

FIG. 2 illustrates an electrical model of the plasma reactor employed bythe measurement instrument.

FIG. 3A illustrates the structure of the LF section of the measurementinstrument of FIG. 1.

FIG. 3B illustrates the structure of the HF section of the measurementinstrument of FIG. 1.

FIG. 4A illustrates an input phase processor of the LF measurementinstrument section of FIG. 3A.

FIG. 4B illustrates an input phase processor of the HF measurementinstrument section of FIG. 3B.

FIG. 5A illustrates a transmission line transformation processor in themeasurement instrument LF section of FIG. 3A.

FIG. 5B illustrates a transmission line transformation processor in themeasurement instrument HF section of FIG. 3B.

FIG. 6A illustrates a grid-to-ground transformation processor in themeasurement instrument LF section of FIG. 3A.

FIG. 6B illustrates a grid-to-ground transformation processor in themeasurement instrument HF section of FIG. 3B.

FIG. 7A illustrates a grid-to-wafer transformation processor in themeasurement instrument LF section of FIG. 3A.

FIG. 7B illustrates a grid-to-wafer transformation processor in themeasurement instrument HF section of FIG. 3B.

FIG. 8A illustrates a combined transformation processor in themeasurement instrument LF section of FIG. 3A.

FIG. 8B illustrates a combined transformation processor in themeasurement instrument HF section of FIG. 3B.

FIG. 9 illustrates apparatus for providing constants or

factors employed by the measurement instrument of FIG. 1A.

DETAILED DESCRIPTION OF THE INVENTION

ESC With High Contact Force Wafer Cooling:

FIG. 1A illustrates a plasma reactor having a cylindrical side wall 10,a ceiling 12 and a wafer contact-cooling electrostatic chuck (ESC) 14. Apumping annulus 16 is defined between the chuck 14 and the sidewall 10.While the wafer contact-cooling electrostatic chuck 14 may be used inany type of plasma reactor or other reactor (such as thermal processreactor), the reactor in the example of FIG. 1A is of the type in whichprocess gases can be introduced through a gas distribution plate 18 (or“showerhead”) forming a large portion of the ceiling 12. Alternatively,the reactor could have gas distribution inlets 20 (dashed lines) thatare separate from the ceiling 12. While the wafer contact-coolingelectrostatic chuck 14 may be employed in conjunction with any plasmasource (not illustrated in the drawing), such as an inductively coupledRF plasma source, a capacitively coupled RF plasma source or a microwaveplasma source, or a torroidal plasma source. A process gas supply 34 iscoupled to the gas distribution plate 18 (or to the gas injectors 20). Asemiconductor wafer or workpiece 40 is placed on top of the chuck 14. Aprocessing region 42 is defined between the wafer 40 and the ceiling 12(including the gas distribution plate 18).

Plasma RF bias power from a low frequency RF bias power generator 125and from a high frequency RF bias power generator 125′ is appliedthrough an impedance match circuit 130 to the wafer support pedestal 14.A D.C. chucking voltage is applied to the chuck 14 from a chuckingvoltage source 48 isolated from the RF bias power generator 125 by anisolation capacitor 50. The RF power delivered to the wafer 40 from theRF bias power generators 125, 125′ can heat the wafer 40 to temperaturesbeyond 400 degrees C., depending upon the level and duration of theapplied RF plasma bias power. It is believed that about 80% or more ofthe RF power is dissipated as heat in the wafer 40.

The electrostatic chuck 14 of FIG. 2 is a wafer contact-coolingelectrostatic chuck in which the portion of the chuck contacting thewafer is cooled. The wafer contact-cooling electrostatic chuck 14requires no gas cooling source nor internal gas coolant passages to keepthe wafer cool and remove heat from the wafer (although such a featuremay be included nevertheless). Instead, the heat is removed from thewafer at a rate which limits the maximum wafer temperature or the timerate of rise of the wafer temperature during plasma processing, bycooling the chuck 14 itself while maintaining direct high-force contactbetween the wafer 40 and the chuck 14, as will now be described.Alternatively, the chucking voltage may be varied during waferprocessing to vary the selected heat transfer coefficient in order tocontrol wafer temperature to a target value. This latter feature may becarried out by monitoring the wafer temperature and varying the chuckvoltage so as to minimize the difference between the measured wafertemperature and a target temperature. As the measured wafer temperaturerises above a maximum target temperature, the chucking voltage isincreased, and as the measured wafer temperature falls below a targetminimum temperature, the chucking voltage may be decreased. Moreover,the high-force contact cooling of the wafer is able to control wafertemperature even at very high RF bias power levels.

The chuck 14 has a top layer 60, referred to as a puck, consisting ofinsulative or semi-insulative material, such as aluminum nitride oraluminum oxide, which may be doped with other materials to control itselectrical and thermal properties. A metal (molybdenum, for example)wire mesh or metal layer 62 inside of the puck 60 forms a cathode (orelectrode) to which the chucking voltage and RF bias power is appliedvia a coaxial cable 210. The puck 60 may be formed as a ceramic. Or, itmay be formed by plasma or physical deposition processes, or chemicalvapor deposition process or plasma or flame spray coating or othermethod. It is supported on a metal layer 64, preferably consisting of ametal having a high thermal conductivity, such as aluminum. The metallayer 64 rests on a highly insulative layer 66 whose thickness,dielectric constant and dielectric loss tangent are chosen to providethe chuck 14 with selected RF characteristics (e.g., capacitance, lossresistance) compatible with the reactor design and process requirements.A metal base layer 68 is connected to ground. The wafer 40 is held onthe chuck 14 by applying a D.C. voltage from the chucking voltage source48 to the electrode 62. The application of voltage across the insulatorlayer 60 polarizes the insulator 60 and induces an opposite (attractive)image charge in the bottom surface of the wafer 40. In the case of asemi-insulator layer 60, in addition to inducing image charge in thebottom surface of the wafer, charge from the electrode 62 migratesthrough the semi-insulator layer 60 to accumulate very close to the topsurface of the semi-insulator layer 60, for a minimum gap between thecharge and the overlying wafer 40. (The term “semi-insulator” isdiscussed below.) This induces an opposite (attractive) image charge inthe bottom surface of the wafer 40. The effective gap between the twoopposing charge layers is so minimal as a result of the upward chargemigration in the insulator layer 60 that the attractive force betweenthe chuck and the wafer 40 is very large for a relatively small appliedchucking voltage. For example, a chucking voltage of only 300 volts D.C.on the electrode 62 produces a chucking force across the wafer 40equivalent to a pressure of about 100 Torr. The puck semi-insulatorlayer 60 therefore is formed of a material having a desired chargemobility, so that the material is not a perfect insulator (hence, theterm “semi-insulator”). This semi-insulator material, although not aperfect insulator, may also not be a typical semiconductor, in somecases. In any case, the charge induced by the chucking voltage on theelectrode 62 is mobile in the semi-insulator material of the puck layer60, and therefore it may be said that the puck semi-insulator layer 60is formed of a “charge mobile” material. One example of a materialsuitable for the puck semi-insulator or charge mobile layer 60 isaluminum nitride. Another example is aluminum oxide, which mayoptionally be doped to increase charge mobility. For example, the dopantmaterial may be titanium dioxide.

RF bias power from the RF bias power generators 125, 125′ may be appliedthrough the impedance match circuit 130 to the electrode 62 or,alternatively, to the metal layer 64 for RF coupling through thesemi-insulative puck layer 60.

A very high heat transfer coefficient between the wafer 40 and the puck60 is realized by maintaining a very high chucking force. A suitablerange for this force depends upon the anticipated heat loading of thewafer, and will be discussed later in this specification. The heattransfer coefficient (having units of Watts/m²° K or heat flux densityfor a given temperature difference) of the wafer-to-puck contactingsurfaces is adequate to remove heat at the rate heat is deposited on thewafer. Specifically, the heat transfer coefficient is adequate becauseduring plasma processing it either limits the wafer temperature below aspecified maximum temperature or limits the time rate of rise of thewafer temperature below a maximum rate of rise. The maximum wafertemperature may be selected to be anywhere in a practical range from onthe order to 100 degrees C. or higher, depending upon the heat load. Themaximum rate of heat rise during processing may be anywhere in a rangefrom 3 to 20 degrees per second. Specific examples may be 20 degrees persecond, or 10 degrees per second or 3 degrees per second. By comparison,if the wafer is un-cooled, the rate of heat rise may be 86.7 degrees persecond in the case of a typical 300 mm silicon wafer with a heat load of7500 Watts, 80% of which is absorbed by the wafer. Thus, the rate oftemperature rise is reduced to one-fourth of the un-cooled rate of heatrise in one embodiment of the invention.

Such performance is accomplished, first, by maintaining the puck at asufficiently low temperature (for example, about 80° C. below the targetwafer temperature), and second, by providing the top surface of the puck60 with a sufficiently smooth finish (e.g., on the order of ten's ofmicro-inches RMS deviation, or preferably on the order of micro-inchesRMS deviation). For this purpose, the top surface 60 a of the puck 60can be highly polished to a finish on the order of about 2 micro-inchesRMS deviation, for example. Furthermore, heat is removed from the puck60 by cooling the metal layer 64. For this reason, internal coolantpassages 70 are provided within the metal layer 64 coupled to a coolantpump 72 and heat sink or cooling source 74. In an alternativeembodiment, the internal cooling passages 70 may extend into the puck 60or adjacent its back surface in addition or instead of extending throughthe metal layer 64. In any case, the coolant passages 70 are thermallycoupled to the puck 60, either directly or through the metal layer 64,and are for cooling the puck 60. The coolant liquid circulating throughthe internal passages 70 can be water, ethylene glycol or a mixture, forexample. Alternatively, the coolant may be a perfluorinated heattransfer liquid such as “fluorinert” (made by 3M company). Unlike theinternal gas coolant passages of conventional chucks, this featurepresents little or no risk of arcing in the presence of high RF biaspower applied to the chuck 14 by the RF bias power generator 125.

One advantage of such contact-cooling of the wafer over the conventionalmethod employing a coolant gas is that the thermal transfer efficiencybetween the coolant gas and each of the two surfaces (i.e., the pucksurface and the wafer bottom surface) is very limited, in accordancewith the thermal accommodation coefficient of the gas with the materialsof the two surfaces. The heat transfer rate is attenuated by the productof the gas-to-wafer thermal accommodation coefficient and thegas-to-puck thermal accommodation coefficient. If both coefficients areabout 0.5 (as a high rough estimate), then the wafer-gas-puck thermalconductance is attenuated by a factor of about 0.25. In contrast, thecontact-cooling thermal conductance in the present invention hasvirtually no such attenuation, the thermal accommodation coefficientbeing in effect unity for the chuck 14 of FIGS. 1A-4. Therefore, thecontact cooling electrostatic chuck 14 can outperform conventionalelectrostatic chucks (i.e., electrostatic chucks that that employ gascooling) by a factor of about four (or more) with sufficiently highattractive electrostatic force between wafer and puck. We have observedin preliminary tests an improvement of about a factor of three.

The heat transfer coefficient between the wafer 40 and the puck 60 inthe wafer contact-cooling electrostatic chuck 14 is affected by the pucktop surface finish and the chucking force. These parameters can beadjusted to achieve the requisite heat transfer coefficient for aparticular environment. An important environmental factor determiningthe required heat transfer coefficient is the applied RF bias powerlevel. It is believed that at least 80% of the RF bias power from thebias generator 125 is dissipated as heat in the wafer 40. Therefore, forexample, if the RF bias power level is 7500 Watts and 80% of the RF biaspower from the bias generator 125 is dissipated as heat in the wafer 40,if the wafer area is 706 cm² (300 mm diameter wafer) and if a 80 degreesC. temperature difference is allowed between the wafer 40 and the puck60, then the required heat transfer coefficient is h=7500×80% Watts/(706cm²×80 degrees K), which is 1071 Watts/m²° K. For greater RF bias powerlevels, the heat transfer coefficient can be increased by augmenting anyone or both of the foregoing factors, namely the temperature drop acrossthe puck, the chucking force or the smoothness of the puck surface. Sucha high heat transfer coefficient, rarely attained in conventionalelectrostatic chucks, is readily attained in the electrostatic chuck 14of FIG. 2 by applying a sufficiently high chucking voltage, on the orderof 1 kV, for example.

In addition, the heat transfer is improved by providing more pucksurface area available for direct contact with the wafer backside. In aconventional chuck, the puck surface available for wafer contact isgreatly reduced by the presence of open coolant gas channels machined,ground or otherwise formed in the puck surface. These channels occupy alarge percentage of the puck surface.

Dual Bias Power Frequencies for Enhanced Etch Performance:

The reactor of FIG. 1A employs two different bias power frequencies,namely f1 and f2, in order to optimize etch performance. The first biasfrequency f1 is a low frequency (LF) RF signal, such as 2 MHz, and issufficiently low for ions at the plasma sheath to follow theoscillations of its electric field. Since some of the ions that are inphase with the LF electric field will be accelerated across the sheathwhile other ions that are out of phase with the LF electric field willbe decelerated across the plasma sheath, the LF bias source provides arelatively wide spectrum of ion energy. For example, for a nominal RFbias level of 1000 volts at 2 MHz, the ion energy will range from about300 eV to 1800 eV. The second bias frequency f2 is a high frequency (HF)RF signal that is too high to be followed by ions at the plasma sheath,so that the ion energy distribution produced by the HF bias source isrelatively narrow and is centered at an average value corresponding tohalf the peak-to-peak voltage. The combination of the narrow ion energydistribution of the HF bias source (of frequency f2) and the broad ionenergy distribution of the LF bias source (of frequency f1) produces anion energy distribution extending from the average ion energy levelgenerated by the HF bias source to the higher ion energy levelsgenerated by the LF bias source. It is believed that such higher ionenergy levels enhance etch performance. The problem is thatintermodulation products between the two bias frequencies, f1 and f2,make it seemingly impossible to accurately measure the net wafervoltage.

Wafer Contact Force Feedback Control:

Conventional sensing circuits 132 within the impedance match circuit 130have output terminals 133 providing signals indicating, respectively,the low frequency voltage V(f1), current I(f1) and (optionally) powerP_(bias)(f1), and the high frequency voltage V(f2), current I(f2) and(optionally) power P_(bias)(f2) furnished at the output of the impedancematch circuit 130 to the wafer support pedestal 14. A measurementinstrument 140 uses the signals from the output terminals 133 to measurethe voltage on the wafer 40. The measurement instrument 140 employsprocesses based upon an electrical model of the reactor 100 discussedbelow. A processor 80 periodically computes the D.C. voltage of thewafer 40. A subtractor 82 computes the net chucking voltage as thedifference between the D.C. wafer voltage and the D.C. voltage appliedto the pedestal 14 by the chucking voltage source 48. A feedbackcontroller 84 compares the net chucking voltage provided by thesubtractor 82 with a desired net chucking voltage to determine an error,and applies a corrective signal to change the D.C. output of the D.C.voltage supply 48 so as to reduce this error. The desired net chuckingvoltage may be furnished by a wafer temperature control processor thattranslates a user-commanded wafer temperature to a desired net chuckingvoltage.

Measurement of the Wafer Voltage With a Correction for IntermodulationProducts of f1 and f2:

Referring to FIG. 1B, a processor 90 determines the voltage V_(junction)at the electrode or grid 62 by multiplying the voltage V_(in) andcurrent I_(in) measured at the input to the cable 210 by respectiveconstants and summing the two products. As disclosed in co-pending U.S.application Ser. No. 10/440,364 filed May 16, 2003 by Daniel Hoffman andassigned to the present assignee, this multiplication and summing takesthe following form:V_(in){ cos h [(V_(ch))(−length)]}+I_(in){Z_(ch) sinh[(V_(ch))(−length)]}so that one constant is cos h [(V_(ch))(−length)] and the other constantis Z_(ch) sin h [(V_(ch))(−length)]. These two constants are referred toherein as K1 and K2, respectively. Z_(ch) is the characteristicimpedance of the coaxial cable 210, V_(ch) is the complex phase velocityof the cable 210 and “length” is the cable length. The voltage V_(wafer)at the wafer 40 is obtained by incorporating into each of the constantsthe factor Z_(wafer)/Z_(grid), in accordance with the operation of theprocessor 520 of FIG. 5A and the processor 830 of FIG. 8A of thereferenced application. Z_(wafer) is the impedance between the grid 62and the wafer 120 while Z_(grid) is the impedance between the grid 62and ground. With this correction factor incorporated into the constants,they become as follows:K1=(Z _(wafer) /Z _(grid))cos h [(V _(ch))(−length)]K2=(Z _(wafer) /Z _(grid))Z _(ch) sin h [(V _(ch))(−length)].

The foregoing is valid for a single bias frequency, in accordance withthe referenced application. Each of the parameters Z_(wafer), Z_(grid)and V_(ch) is evaluated at the particular bias frequency, so that K1 andK2 depend upon frequency.

In the reactor of FIG. 1A, there are two bias sources 125, 125′providing bias power at the LF frequency f1 and at the HF frequency f2,respectively. Therefore two processors 90 and 91 of FIG. 1B separatelycompute the wafer voltages at the respective bias frequencies f1, f2,employing the constants K1, K2 evaluated at the different biasfrequencies, as follows: K1(f1), K2(f1), K1(f2), K2(f2). The measurementinstrument 132 provides the LF input voltage V_(in)(f1) and inputcurrent I_(in)(f1) to the processor 90 and the HF input voltageV_(in)(f2) and input current I_(in)(f2) to the processor 92. The LFprocessor 90 employs the LF constants K1(f1), K2(f1) while the HFprocessor 91 employs the HF constants K1(f2), K2(f2), to produce the LFwafer voltage V_(wafer)(f1) and the HF wafer voltage V_(wafer)(f2),respectively. The two RF wafer voltages, V_(wafer)(f1) andV_(wafer)(f2), are then used to determine the measured D.C. wafervoltage as follows. First, wafer D.C. voltages at the two frequencies,V_(DC)(f1), V_(DC)(f2) are determined as the RMS values of the LF and HFwafer voltages, V_(wafer)(f1), V_(wafer)(f2), by processors 92, 93,respectively.

In order to determine the total D.C. voltage on the wafer attributableto both frequency components, we have found significant errors occurwhen a simple addition of the two frequency components,V_(DC)(f1)+V_(DC)(f2), is employed. This is because such a simpleaddition does not take into account the effects of intermodulationbetween the two bias frequencies. As discussed earlier in thisspecification, the error can exceed the capacity of the chucking D.C.voltage supply 48. Therefore, a correction factor is subtracted from theresult, the correction factor containing the product of the two D.C.voltage components V_(DC)(f1), V_(DC)(f2). The combination of the simplesum and the correction factor is carried out by a processor 94 todetermine total D.C. voltage on the wafer:V _(DC)(total)=V _(DC)(f1)+V _(DC)(f2)+E{[V _(DC)(f1)][V _(DC)(f2)]}^(F)

Where E and F are constants. Theoretically, F=½ and E=1, but inpractical application we have found superior results are obtained withF=0.43 and E=1. This provides a highly accurate measurement of the D.C.voltage on the wafer, V_(DC)(wafer), which is the input to the feedbackcontrol loop 82, 84, 48 governing the ESC clamping force applied to thewafer. The subtractor 82 determines the net wafer clamping voltage,ΔV_(DC), as the difference between the measured D.C. wafer voltage fromthe processor 80, V_(DC)(total), and the D.C. voltage output by the D.C.chuck voltage supply 48. The feedback controller 84 compares this valuewith a desired clamping voltage to determine an error, and changes theoutput of the ESC D.C. voltage supply 48 so as to reduce this error.

Measurement of the Wafer Voltage Based Upon the ElectricalCharacteristics of the Chamber:

FIG. 2 depicts an electrical model of the plasma reactor of FIG. 1A thatdefines electrical parameters of the certain reactor components used inthe measurement instrument 140 to determine voltage on the wafer 40 fromRF voltage and current at the output of the impedance match 130. In themodel of FIG. 2, the electrostatic chuck (ESC) 14 includes thedielectric puck 60 containing the electrode or conductive grid 62, thepuck 60 being divided by the electrode 62 into a thin overlyingdielectric layer 115-2 and an underlying dielectric layer 115-3. Thelayer 115-3 can model the combination of the layers 60 (lower portion),64 and 66 that separate the electrode 62 from the grounded metal base68. FIG. 2 also shows the coaxial cable 210 connecting the output of theimpedance match circuit 130 to the grid 62. The coaxial cable 210 has aninner conductor 212 and an outer conductor 214.

The electrical model depicted in FIG. 2 characterizes the electricalproperties of the plasma reactor, which are readily determined usingconventional techniques. Specifically, the coaxial transmission line orcable 210 is characterized by three quantities: (1) its length, (2)Z_(ch), its characteristic impedance, and (3) V_(ch), its complex phasevelocity in the transmission line equation. Since the complex phasevelocity V_(ch) depends upon the frequency of the signal propagatingthrough the coaxial cable, it will be referred to herein as V_(ch)(f) inorder to indicate its dependency upon frequency. The ESC 14 ischaracterized by electrical properties of the overlying and underlyingdielectric layers 115-2 and 115-3. Specifically, the underlyingdielectric layer 115-3 has a capacitance C_(D), which is a function of(1) the dielectric constant, ∈_(D), of the dielectric layer 115-3, and(2) the conductive loss component of the dielectric layer 115-3,tan_(D), (3) the thickness, gap, of the dielectric layer 115-3 and (4)the radius of the wafer 40. The conductive loss component tan_(D)depends upon the frequency of the signal being coupled through thedielectric layer, and therefore it will be referred to herein astan_(D)(f) in order to indicate its dependency upon frequency. Theoverlying dielectric layer 115-2 has a capacitance C_(P) which is afunction of (1) the thickness, gap_(P), of the dielectric layer 115-2,(2) the dielectric constant, ∈_(P), of the dielectric layer 115-2 and(3) the conductive loss component of the dielectric layer 115-2,tan_(P). The conductive loss component tan_(P) depends upon thefrequency of the signal being coupled through the dielectric layer, andtherefore it will be referred to herein as tan_(P)(f) in order toindicate its dependency upon frequency.

In one implementation, the measurement instrument 140 of FIG. 1A can bedivided into two sections 140 a, 140 b, dedicated to the measurement ofthe respective components of the wafer voltage at the frequencies f1,f2, respectively. For this purpose, the output signals from the sensor132 pertaining to the LF components (i.e., V(f1), I(f1), P(f1)) areprovided to the measurement instrument section 140 a, while the outputsignals from the sensor 132 pertaining to the HF components (i.e.,V(f1), I(f1), P(f1)) are provided to the measurement instrument section140 b. The two sections 140 a, 140 b will therefore employ differentvalues of the frequency-dependent model parameters referred to above.Thus, the measurement instrument section 140 a uses V_(ch)(f1),tan_(D)(f1), tan_(P)(f1), which are the values of thesefrequency-dependent parameters evaluated at the LF frequency f1.Likewise, the measurement instrument section 140 b uses V_(ch)(f2),tan_(D)(f2), tan_(P)(f2), which are the values of thesefrequency-dependent parameters evaluated at the HF frequency f2. FIGS.3A and 3B illustrates the structure of the respective measurementinstrument sections 140 a, 140 b of FIG. 1A.

The LF Measurement Instrument Section 140 a:

Referring to FIG. 3A, in the measurement instrument section 140 a, aninput phase processor 310 receives the low frequency (LF) P_(bias)(f1),V(f1) and I(f1) signals from the impedance match sensing circuit 132 ofFIG. 1A and produces respective signals indicating an LF input currentI_(in)(f1) and an LF input voltage V_(in)(f1) at the near end of thecoaxial cable 210 (i.e., the end nearest the impedance match circuit130). [In one embodiment, the input phase processor 310 is not employed,so that the LF input current and voltage, I_(in)(f1), V_(in)(f1), arethe same as the LF voltage and current, V(f1), I(f1), from the sensor132. This simplification avoids the complications of computing phase asis done in the processor 310.] A transmission line transformationprocessor 320 uses the characteristic impedance Z_(ch) and the complexphase velocity or loss coefficient V_(ch)(f1) from an electrical model330 of the coaxial cable 210 to transform from I_(in) and V_(in) at thenear cable end to a voltage V_(junction) at the far cable end, i.e., atthe junction between the coaxial cable 210 and the grid 62. Agrid-to-ground transformation processor 340 takes radius, gap, ∈_(D) andtan_(D)(f1) from a model 345 of the grid-to-ground capacitance andproduces a dielectric resistance R_(D)(f1) and dielectric capacitanceC_(D). A grid-to-wafer transformation processor 350 takes radius,gap_(P), ∈_(P) and tan_(P)(f1) from a model 355 of the grid-to-wafercapacitance and produces a plasma resistance R_(P)(f1) and a plasmacapacitance C_(P). A combined transformation processor 360 accepts theoutputs of all the other processors 320, 340, 350 and computes the wafervoltage V_(wafer)(f1).

In summary, electrical measurements are made at the output of theimpedance match circuit 130. The transmission line transformationprocessor 320 transforms these measurements at the near end of the cable210 to a voltage at the far end. The grid to ground transformationprocessor 340 provides the transformation from the ground plane 64 nearthe far end of the cable to the conductive grid 62. The grid-to-wafertransformation processor 350 provides the transformation from theconductive grid 62 to the wafer 40.

The transmission line model 330, the model of the grid-to-groundcapacitance 345 and the model 355 of the grid-to-wafer capacitance arenot necessarily a part of the measurement instrument 140. Or, they maybe memories within the measurement instrument 140 that store,respectively, the coaxial cable parameters (V_(ch)(f1) and Z_(ch)), thegrid-to-ground capacitance parameters (gap, ∈_(D), tan_(D)(f1) andradius) and the grid-to-wafer capacitance parameters (gap_(P), ∈_(P),tan_(P)(f1) and radius).

FIG. 4A illustrates the structure of the input phase processor 310 ofFIG. 3A. A delivered power arithmetic logic unit (ALU) 410 computesdelivered power P(f1) from the outputs I(f1) and P_(bias)(f1) of theimpedance match sensing circuit 132 as P_(bias)(f1)−(0.15)I(f1)². Aphase angle ALU 420 computes phase angle θ(f1) from the delivered powerP(f1) and from V(f1) and I(f1) as cos⁻¹[P(f1)/V(f1)I(f1)]. An impedanceALU 430 computes the complex impedance Z(f1) as (V(f1)/I(f1))e^(iθ),where i=(−1)^(1/2). An input current ALU 440 computes the input currentI_(in)(f1) to the coaxial cable 210 as [P(f1)/Re(Z(f1))]^(1/2). An inputvoltage ALU 450 computes the input voltage V_(in)(f1) to the coaxialcable 210 as Z(f1)I_(in)(f1).

FIG. 5A illustrates the structure of the transmission linetransformation processor 320 of FIG. 3A. The transmission line processorreceives I_(in)(f1) and V_(in)(f1) as inputs from the input phaseprocessor 310 of FIG. 4A and uses the transmission line model parametersV_(ch)(f1) and Z_(ch) (from the transmission line model or memory 330 ofFIG. 3A) to compute the junction voltage at the cable out end,V_(junction)(f1) and admittance Y_(junction)(f1) as follows: A junctioncurrent ALU 510 computes the current I_(junction)(f1) at the junction ofthe coaxial cable 210 and the grid 62 (FIG. 1A) as:I_(in)(f1){ cos h [V_(ch)(f1)(−length)]}+V_(in)(f1){(1/Z_(ch))sin h[V_(ch)(f1)(−length)]}

A junction voltage ALU 520 computes the voltage V_(junction)(f1) at thejunction between the coaxial cable 210 and the grid 62 as:V_(in)(f1){ cos h [(V_(ch)(f1)(−length)]+I_(in)(f1){Z_(ch) sin h[V_(ch)(f1)(−length)]}

A divider 530 receives I_(junction) and V_(junction) computesY_(junction) as I_(junction)/V_(junction). Each of the electricalquantities in the foregoing computations (current, voltage, impedance,admittance, etc.) may be a complex number having both a real part and animaginary part.

FIG. 6A illustrates the structure of the grid-to-ground transformationprocessor 340 of FIG. 3A. The grid-to-ground transformation processor340 receives the parameters gap, ∈_(D), tan_(D)(f1) and rad (the waferradius) from the grid-to-ground model or memory 345 of FIG. 3A computesthe dielectric resistance R_(D)(f1) and the dielectric capacitanceC_(D). The dielectric capacitance C_(D) is computed by a CD ALU 610 asfollows:(∈₀)(∈_(D))π(rad)²/gapwhere ∈₀ is the electrical permittivity of free space. An RD ALU 620uses the value of C_(D) from the CD ALU 610 and computes the dielectricresistance R_(D)(f1) as follows:(tan_(D)(f1))/(2π)(f1)C_(D) gap²)

FIG. 7A illustrates the structure of the grid-to-wafer transformationprocessor 350 of FIG. 3A. The grid-to-wafer transformation processor 350receives the parameters gap_(P), ∈_(P), tan_(P)(f1) and rad from thegrid-to-wafer model or memory 355 of FIG. 3A and computes the plasmaresistance R_(P)(f1) and the plasma capacitance C_(P). The plasmacapacitance C_(P) is computed by a CP ALU 710 as follows:(∈₀)(∈_(P))π(rad)²/gap_(P)where ∈₀ is the electrical permittivity of free space. An RP ALU 720uses the value of C_(P) from the CP ALU 710 and computes the plasmaresistance R_(P)(f1) as follows:(tan_(P)(f1))/((2π)(f1)C_(P) gap_(D) ²)

FIG. 8A illustrates the structure of the combined transformationprocessor 360 of FIG. 3A. The combined transformation processor 360receives the parameters R_(D)(f1), C_(D) from the processor 340 of FIG.3A, receives the parameters R_(P)(f1), C_(P) from the processor 350 ofFIG. 3A and receives the parameter Y_(junction) from the processor 320of FIG. 3A. A grid impedance ALU 810 computes Z_(grid) (the impedance atthe grid 62) as follows:[Y_(junction)(f1)−1/(R_(D)(f1)+(1/(i2π(f1)C_(D))))]⁻¹

A wafer impedance ALU 820 uses the output of the grid impedance ALU 810to compute Z_(wafer) (the impedance at the wafer 40 of FIG. 2) asfollows:Z_(grid)(f1)−1/(R_(P)(f1)+(1/(i2π(f1)C_(P))))

A wafer voltage ALU 830 uses the outputs of both ALUs 810 and 820 andV_(junction)(f1) from the divider 530 of FIG. 5A to compute the voltageon the wafer 120 of FIG. 2, V_(wafer)(f1), asV_(junction)(f1)Z_(wafer)(f1)/Z_(grid)(f1).

It should be noted that the exact computation of Z_(grid)(f1) dependsupon both V_(in)(f1) and I_(in)(f1) in respective transmission lineequations for the voltage and current V_(junction)(f1), I_(junction)(f1)as described above, so that Z_(grid)(f1) is not necessarily a constant.In order to simplify the computation of the wafer voltage V_(wafer)(f1),the factor Z_(wafer)(f1)/Z_(grid)(f1) is ignored (assigned a value ofunity) Alternatively, the computation may be simplified by choosing anaverage value of Z_(grid)(f1) within an applicable operating processwindow as a constant to replace the exact computation of Z_(grid)(f1) inthe determination of V_(wafer)(f1). With this simplification, the factorZ_(wafer)(f1)/Z_(grid)(f1) becomes a constant, so that the determinationof the wafer voltage V_(wafer)(f1) by ALU 380 becomes multiplication ofthe cable/electrode junction voltage V_(junction)(f1) by a constant(i.e., by the factor Z_(wafer)(f1)/Z_(grid)(f1). This may reduce theaccuracy slightly but has the advantage of simplifying the computationof V_(wafer)(f1).

If desired, a processor 840 produces a measured wafer current bydividing the wafer voltage V_(wafer)(f1) by the wafer impedanceZ_(wafer)(f1).

The HF Measurement Instrument Section 140 b:

Referring to FIG. 3B, in the measurement instrument section 140 b, aninput phase processor 310′ receives the high frequency (HF)P_(bias)(f2), V(f2) and I(f2) signals from the impedance match sensingcircuit 132 of FIG. 1A and produces respective signals indicating an HFinput current I_(in)(f2) and an HF input voltage V_(in)(f2) at the nearend of the coaxial cable 210 (i.e., the end nearest the impedance matchcircuit 130). [In one embodiment, the input phase processor 310′ is notemployed, so that the HF input current and voltage, I_(in)(f2),V_(in)(f2), are the same as the HF voltage and current, V(f2), I(f2),from the sensor 132.] A transmission line transformation processor 320′uses the characteristic impedance Z_(ch) and the complex phase velocityor loss coefficient V_(ch)(f2) from an electrical model 330 of thecoaxial cable 210 to transform from I_(in) and V_(in) at the near cableend to a voltage V_(junction) at the far cable end, i.e., at thejunction between the coaxial cable 210 and the grid 62. A grid-to-groundtransformation processor 340′ takes radius, gap, ∈_(D) and tan_(D)(f2)from a model 345 of the grid-to-ground capacitance and produces adielectric resistance R_(D)(f2) and dielectric capacitance C_(D). Agrid-to-wafer transformation processor 350′ takes radius, gap_(P), ∈_(P)and tan_(P)(f2) from a model 355 of the grid-to-wafer capacitance andproduces a plasma resistance R_(P)(f2) and a plasma capacitance C_(P). Acombined transformation processor 360′ accepts the outputs of all theother processors 320′, 340′, 350′ and computes the wafer voltageV_(wafer)(f2).

In summary, electrical measurements are made at the output of theimpedance match circuit 130. The transmission line transformationprocessor 320′ transforms these measurements at the near end of thecable 210 to a voltage at the far end. The grid to ground transformationprocessor 340′ provides the transformation from the ground plane 64 nearthe far end of the cable to the conductive grid 62. The grid-to-wafertransformation processor 350′ provides the transformation from theconductive grid 62 to the wafer 40.

The transmission line model 330′, the model of the grid-to-groundcapacitance 345 and the model 355 of the grid-to-wafer capacitance arenot necessarily a part of the measurement instrument 140. Or, they maybe memories within the measurement instrument 140 that store,respectively, the coaxial cable parameters (V_(ch)(f2) and Z_(ch)), thegrid-to-ground capacitance parameters (gap, ∈_(D), tan_(D)(f2) andradius) and the grid-to-wafer capacitance parameters (gap_(P), ∈_(P),tan_(P)(f2) and radius).

FIG. 4B illustrates the structure of the input phase processor 310′ ofFIG. 3B. A delivered power arithmetic logic unit (ALU) 410′ computesdelivered power P(f2) from the outputs I(f2) and P_(bias)(f2) of theimpedance match sensing circuit 132 as P_(bias)(f2)−(0.15)I(f2)². Aphase angle ALU 420′ computes phase angle θ(f2) from the delivered powerP(f2) and from V(f2) and I(f2) as cos⁻¹[P(f2)/V(f2)I(f2)]. An impedanceALU 430′ computes the complex impedance Z(f2) as (V(f2)/I(f2))e^(iθ),where i=(−1)^(1/2). An input current ALU 440′ computes the input currentI_(in)(f2) to the coaxial cable 210 as [P(f2)/Re(Z(f2))]^(1/2). An inputvoltage ALU 450′ computes the input voltage V_(in)(f2) to the coaxialcable 210 as Z(f2) I_(in)(f2).

FIG. 5B illustrates the structure of the transmission linetransformation processor 320′ of FIG. 3B. The transmission lineprocessor receives I_(in)(f2) and V_(in)(f2) as inputs from the inputphase processor 310′ of FIG. 4B and uses the transmission line modelparameters V_(ch)(f2) and Z_(ch) (from the transmission line model ormemory 330′ of FIG. 3B) to compute the junction voltage at the cable outend, V_(junction)(f2) and admittance Y_(junction)(f2) as follows: Ajunction current ALU 510′ computes the current I_(junction)(f2) at thejunction of the coaxial cable 210 and the grid 62 (FIG. 1A) as:I_(in)(f2){ cos h [V_(ch)(f2)(−length)]}+V_(in)(f2){(1/Z_(ch))sin h[V_(ch)(f2)(−length)]}.

A junction voltage ALU 520′ computes the voltage V_(junction)(f2) at thejunction between the coaxial cable 210 and the grid 62 as:V_(in)(f2){ cos h [(V_(ch)(f2)(−length)]+I_(in)(f2){Z_(ch) sin h[V_(ch)(f2)(−length)]}.

A divider 530′ receives I_(junction) and V_(junction) computesY_(junction) as I_(junction)/V_(junction). Each of the electricalquantities in the foregoing computations (current, voltage, impedance,admittance, etc.) may be a complex number having both a real part and animaginary part.

FIG. 6B illustrates the structure of the grid-to-ground transformationprocessor 340′ of FIG. 3B. The grid-to-ground transformation processor340′ receives the parameters gap, ∈_(D), tan_(D)(f2) and rad (the waferradius) from the grid-to-ground model or memory 345 of FIG. 3B computesthe dielectric resistance R_(D)(f2) and the dielectric capacitanceC_(D). The dielectric capacitance C_(D) is computed by a CD ALU 610′ asfollows:(∈₀)(∈_(D))π(rad)²/gapwhere ∈₀ is the electrical permittivity of free space. An RD ALU 620′uses the value of C_(D) from the CD ALU 610′ and computes the dielectricresistance R_(D)(f2) as follows:(tan_(D)(f2))(2π)(f1)C_(D) gap²)

FIG. 7B illustrates the structure of the grid-to-wafer transformationprocessor 350′ of FIG. 3B. The grid-to-wafer transformation processor350′ receives the parameters gap_(P), ∈_(P), tan_(P)(f2) and rad fromthe grid-to-wafer model or memory 355 of FIG. 3B and computes the plasmaresistance R_(P)(f2) and the plasma capacitance C_(P). The plasmacapacitance C_(P) is computed by a CP ALU 710′ as follows:(∈₀)(∈_(P))π(rad)²/gap_(P)where ∈₀ is the electrical permittivity of free space. An RP ALU 720′uses the value of C_(P) from the CP ALU 710′ and computes the plasmaresistance R_(P)(f2) as follows:(tan_(P)(f2))/((2π)(f1)C_(P) gap_(D) ²)

FIG. 8B illustrates the structure of the combined transformationprocessor 360′ of FIG. 3B. The combined transformation processor 360′receives the parameters R_(D)(f2), C_(D) from the processor 340′ of FIG.3B, receives the parameters R_(P)(f2), C_(P) from the processor 350′ ofFIG. 3B and receives the parameter Y_(junction) from the processor 320′of FIG. 3B. A grid impedance ALU 810′ computes Z_(grid) (the impedanceat the grid 62) as follows:[Y_(junction)(f2)−1/(R_(D)(f2)+(1/(i2π(f1)C_(D))))]⁻¹

A wafer impedance ALU 820′ uses the output of the grid impedance ALU810′ to compute Z_(wafer) (the impedance at the wafer 120 of FIG. 2) asfollows:Z_(grid)(f2)−1/(R_(P)(f2)+(1/(i2π(f1)C_(P))))

A wafer voltage ALU 830′ uses the outputs of both ALUs 810′ and 820′ andV_(junction)(f2) from the divider 530′ of FIG. 5B to compute the voltageon the wafer 40 of FIG. 2, V_(wafer)(f2) asV_(junction)(f2)Z_(wafer)(f2)/Z_(grid)(f2).

It should be noted that the exact computation of Z_(grid)(f2) dependsupon both V_(in)(f2) and I_(in)(f2) in respective transmission lineequations for the voltage and current V_(junction)(f2), I_(junction)(f2)as described above, so that Z_(grid)(f2) is not necessarily a constant.In order to simplify the computation of the wafer voltage V_(wafer)(f2),the factor Z_(wafer)(f2)/Z_(grid)(f2) is ignored (assigned a value ofunity). Alternatively, in order to simplify the calculation, an averagevalue of Z_(grid)(f2) within an applicable operating process window maybe chosen as a constant to replace the exact computation of Z_(grid)(f2)in the determination of V_(wafer)(f2). With this simplification, thefactor Z_(wafer)(f2)/Z_(grid)(f2) becomes a constant, so that thedetermination of the wafer voltage V_(wafer)(f2) by ALU 830′ becomesmultiplication of the cable/electrode junction voltage V_(junction)(f2)by a constant (i.e., by the factor Z_(wafer)(f2)/Z_(grid)(f2)). This mayreduce the accuracy slightly but has the advantage of simplifying thecomputation of V_(wafer)(f2).

If desired, the wafer current at f2 may be measured by a processor 840′that divides the wafer voltage V_(wafer)(f2) by the wafer impedanceZ_(wafer)(f2).

Determination of the Constants Used by the Processors of FIG. 1A:

The two measurement instrument sections 140 a, 140 b provide the LF andHF components of the wafer voltage V_(wafer)(f1), V_(wafer)(f2),respectively. These two components are used in the processor of FIG. 1Bto compute the total wafer D.C. voltage while accounting for voltagelosses due to intermodulation between the two frequencies, as describedabove with reference to FIG. 1B. The LF constants K1(f1), K2(f1)employed by the processor 90 of FIG. 1B to determine the LF component ofthe wafer voltage are defined in accordance with the disclosure of FIGS.3A, 4A, 5A, 6A, 7A and 8A as follows:K1(f1)=[Z _(wafer)(f1)/Z _(grid)(f1)] cos h [V _(ch)(f1)(−length)]K2(f1)=[Z _(wafer)(f1)/Z _(grid)(f1)]Z _(ch) sin h [V_(ch)(f1)(−length)]

The HF constants K1(f2), K2(f2) employed by the processor 91 of FIG. 1Bto determine the HF component of the wafer voltage are defined inaccordance with the disclosure of FIGS. 3B, 4B, 5B, 6B, 7B and 8B asfollows:K1(f2)=[Z _(wafer)(f2)/Z _(grid)(f2)] cos h [V _(ch)(f2)(−length)]K2(f2)=[Z _(wafer)(f2)/Z _(grid)(f2)]Z _(ch) sin h [V_(ch)(f2)(−length)]

FIG. 9 depicts processors 95, 96, 97, 98 for producing the constantsK1(f1), K2(f1), K1(f2), K2(f2), respectively. For the processors 95 and96, the values of Z_(wafer)(f1) and Z_(grid)(f1) come from theprocessors 820 and 810, respectively (of FIG. 8A), as indicated in FIG.9. For the processors 97 and 98, the values of Z_(wafer)(f2) andZ_(grid)(f2) come from the processors 820′ and 810′ (of FIG. 8B)respectively, as indicated in FIG. 9. These constants may be stored inthe registers 90 a, 90 b, 91 a, 91 b, respectively, of FIG. 1B.

In a highly efficient implementation, phase information from the sensor132 is not required. In this implementation, the phase processor 310 isnot employed and the sensor voltages and currents V(f1), I(f1), V(f2),I(f2) are multiplied by the constants stored in the registers 90 a, 90b, 91 a, 91 b in the manner shown in FIG. 1B. In order to ensure thatK1(f1), K2(f1), K1(f2), K2(f2) are true constants, the quantityZ_(grid), is replaced by an average value of Z_(grid) applicable over apredicted operating process window, as mentioned previously in thisspecification.

While each operation performed in the measurement instrument 140 hasbeen described with respect to a separate processor, several of theprocessors within the measurement instrument 140 may be realized in asingle processor whose resources are shared to perform the differentoperations at different times. Or, all of the processors in themeasurement instrument 140 are realized by a single processor that is ashared resource among the different operations performed by themeasurement instrument, so that the measurement instrument 140 may berealized as computer using a central processing unit (CPU) to performall the operations.

The phase processors 310 a, 310 b transform the measured values of thevoltage and current sensed by the sensor 132 into input voltages andcurrents V_(in)(f1), I_(in)(f1), V_(in)(f2), I_(in)(f2). For purposes ofthe claims below, therefore, the phase processors 310 a, 310 b may beconsidered to be part of the sensor 132, so that the outputs V_(in)(f1),I_(in)(f1), V_(in)(f2), I_(in)(f2) of the phase processors 310, 310 bare considered as the measured voltages and currents from the sensor132. In fact, in some cases it may be possible to eliminate or bypassthe phase processors 310.

The use of stored constants K1(f1), K2(f1), K1(f2), K2(f2) greatlysimplifies the computations of the wafer voltage frequency components byreducing them to simple multiplications of the sensed current andvoltage by respective constants and summations of the resultingproducts. This makes it unnecessary to measure phase in order todetermine the wafer voltage.

Some Advantages of the Invention:

The invention may be used with a Johnson-Raybeck electrostatic chuck(ESC) (i.e., the type of ESC depicted in FIG. 1A) in an etch process tocontrol the wafer D.C. voltage so accurately that the bias power may beincreased to the capacity of the ESC (e.g., 10 kW) at a very high wafertemperature (e.g., 60 degrees C.) for straighter etch profile at a verylow chamber pressure (e.g., 5 mT) for better etch selectivity. The heattransfer from the wafer is regulated by controlling the electrostaticclamping force, as described above. Without the accurate measurement andcontrol of the wafer D.C. voltage provided by the present invention, therisk in running such high wafer bias power is that an error in the waferD.C. voltage may cause one of two catastrophic events: (1) if the D.C.wafer voltage is too small, the wafer may be inadequately clamped sothat its temperature rises out of control or the wafer is released fromthe ESC; (2) if the D.C. wafer voltage is too great, the wafer may beover-clamped, leading to process failure by excessive D.C. wafercurrent. The problem is that, while a Johnson-Raybeck ESC can toleratevery high wafer bias power levels (e.g., 10 kW) at low chamber pressure(e.g., 5-10 mT) without breaking down, its insulator layer becomes verylossy at the high temperatures desired for etching, requiring more biaspower to maintain a given D.C. wafer voltage, leading to higher wafercurrent. Before the invention, this problem had to be avoided bylimiting the wafer temperature or the wafer bias voltage (or both) toprevent any error in the wafer D.C. voltage from exceeding thepermissible limits. With the present invention, the wafer D.C. voltage(and current) is monitored in real time with great accuracy in acompletely non-invasive manner. With control feedback to the bias powerlevel, the wafer D.C. voltage and (hence) the wafer clamping voltage canbe taken near the permissible limits (i.e., near maximum wafer currentlimits or near the minimum clamping voltage) with any violation of thoselimits prevented by a real time feedback control system between theinvention's accurate wafer D.C. voltage measurement and the RF biaspower level. As a result, the bias power can be increased to a very highlevel (e.g., 10 kW) at relatively low chamber pressure (e.g., 5 mT) at ahigh wafer temperature (e.g., 60 degrees C.). These process parametervalues define a new high performance etch process window that has beenunattainable until the present invention.

While the invention has been described in detail by specific referenceto preferred embodiments, it is understood that variations andmodifications thereof may be made without departing from the true spiritand scope of the invention.

1. In a plasma reactor having an electrostatic chuck (ESC) supporting awafer to be processed, a method of processing the wafer whilecontrolling an ESC clamping voltage, comprising: applying RF bias powerto said ESC from a bias power source at an input to said ESC andapplying a D.C. voltage at said input to said ESC from a D.C. voltagesource; measuring voltage and current near said input to produce ameasured voltage and a measured current; providing a wafer voltagesignal as a sum of said measured voltage and said measured currentmultiplied by first and second coefficients respectively, said wafervoltage signal representing the voltage on a wafer supported on saidESC; and computing a wafer clamping voltage as a difference between aD.C. component of said wafer voltage signal and said D.C. voltage fromsaid D.C. voltage source, and controlling said D.C. voltage to regulatesaid wafer clamping voltage.
 2. The method of claim 1 wherein the stepof controlling said D.C. voltage comprises minimizing a differencebetween said wafer clamping voltage and a target clamping voltage. 3.The method of claim 2 further comprising selecting said target clampingvoltage in accordance with a desired wafer temperature.
 4. The method ofclaim 1 wherein the step of applying RF bias power comprises applying RFbias power through a coaxial transmission line, and wherein said firstand second coefficients comprise a voltage coefficient and a currentcoefficient, respectively, of a transmission line equation correspondingto said coaxial transmission line.
 5. The method of claim 4 wherein saidwafer support pedestal comprises a conductive grid coupled to the outputend of said coaxial transmission line, and: the step of providing saidwafer voltage signal comprises multiplying said sum by a correctionfactor comprising ratio between a grid-to-wafer impedance, Z_(wafer),and a grid-to-ground impedance, Z_(grid).
 6. The method of claim 5further comprising: producing said voltage and current coefficients inaccordance with said transmission line equation and storing saidcoefficients in a memory associated with said reactor; producing saidgrid-to-ground impedance, Z_(grid), in accordance with a grid-to-groundtransformation corresponding to said transmission line and storing saidgrid-to-ground impedance in said memory; and producing saidgrid-to-wafer impedance, Z_(wafer), in accordance with a grid-to-wafertransformation of said ESC, and storing said grid-to-wafer impedance insaid memory.
 7. In a plasma reactor having a wafer voltage controllerand an electrostatic chuck (ESC) for clamping a wafer to be processed inthe reactor, a method for determining a wafer voltage for use by thecontroller, comprising: applying plasma RF bias power comprising firstand second frequency components, f(1), f(2), respectively, to an inputof said ESC; providing measurement signals representing first and secondfrequency components of a measured voltage and first and secondfrequency components of a measured current at said input of said ESC;providing first and second frequency components of a wafer voltagesignal as, respectively, a first sum of the first frequency componentsof said measured voltage and measured current multiplied by first andsecond coefficients respectively, and a second sum of the secondfrequency components of said measured voltage and measured currentmultiplied by third and fourth coefficients, respectively; and computinga D.C. wafer voltage by combining D.C. components of said first andsecond frequency components of said wafer voltage with a correctionfactor comprising a product of said D.C. components of said first andsecond components of said wafer voltage raised to a selected power andmultiplied by a selected coefficient.
 8. The method of claim 7 whereinsaid selected power is about 0.5 and said selected coefficient is about0.3.
 9. The method of claim 7 wherein said selected power is about 0.43and said selected coefficient is about one.
 10. The method of claim 7wherein said reactor comprises a D.C. supply voltage source connected tosaid ESC, said method further comprising: controlling the voltage ofsaid D.C. supply voltage source of said ESC to govern a wafer clampingvoltage comprising a difference between said D.C. wafer voltage and thevoltage of said D.C. supply voltage of said ESC.
 11. The method of claim10 wherein the step of controlling comprises minimizing a differencebetween said clamping voltage and a target clamping voltage.
 12. Themethod of claim 11 further comprising selecting said target clampingvoltage in accordance with a desired wafer temperature.
 13. The methodreactor of claim 7 wherein: said first and second coefficients comprisea first frequency voltage coefficient and a first frequency currentcoefficient, respectively, of a transmission line equation correspondingto a coaxial transmission line connected to said input of said ESC; andsaid third and fourth coefficients comprise a second frequency voltagecoefficient and a second frequency current coefficient, respectively, ofa transmission line equation corresponding to said coaxial transmissionline.
 14. The method of claim 13 wherein the step of providing saidclamping voltage further comprises: multiplying said first sum by acorrection factor comprising a ratio between a first frequency componentof a grid-to-wafer impedance, Z_(wafer)(f1), and a first frequencycomponent of a grid-to-ground impedance, Z_(grid)(f1); multiplying saidsecond sum by a correction factor comprising a ratio between a secondfrequency component of a grid-to-wafer impedance, Z_(wafer)(f2), and asecond frequency component of a grid-to-ground impedance, Z_(grid)(f2).15. The method of claim 14 further comprising: producing said first andsecond frequency voltage and current coefficients in accordance with atransmission line model and storing said coefficients in a memoryassociated with said reactor; producing said first and second frequencycomponent grid-to-ground impedances, Z_(grid)(f1), Z_(grid)(f2), inaccordance with a grid-to-ground electrical model and storing saidimpedances in said memory; and producing said first and second frequencycomponent grid-to-wafer impedances, Z_(wafer)(f1), Z_(wafer)(f2) inaccordance with a grid-to-wafer electrical model and storing saidimpedances in said memory.
 16. The reactor of claim 7 wherein said firstfrequency component corresponds to a low frequency on the order of a fewMHz, and said second frequency component corresponds to a high frequencyon the order of about 10 MHz, and wherein said correction factorcompensates for intermodulation between said first and second frequencycomponents.